(e.g., Gorenflo, Kilbas, Mainardi and Rogosin [1]}). Therefore,
for \(\lambda \ge 0\) , we have
\(\int ^T_0 \vert \lambda t^{\alpha -1}E_{\alpha ,\alpha }(-\lambda t^{\alpha })\vert dt= \int ^T_0 \lambda t^{\alpha -1}E_{\alpha ,\alpha }(-\lambda t^{\alpha }) dt\) 
\(= -\int ^T_0 \frac{d}{dt}E_{\alpha ,1}(-\lambda t^{\alpha })dt= 1 - E_{\alpha ,1}(-\lambda T^{\alpha }) \le 1. \qquad \mathrm {{(4.10)}}\) 
